Volume 87

Spectral Analysis, DifferentialEquations and MathematicalPhysics: A Festschrift in Honorof Fritz Gesztesy’s 60th Birthday

Helge HoldenBarry SimonGerald TeschlEditors

Volume 87

Spectral Analysis, DifferentialEquations and MathematicalPhysics: A Festschrift in Honorof Fritz Gesztesy’s 60th Birthday

Helge HoldenBarry SimonGerald TeschlEditors

2010 Mathematics Subject Classification. Primary 34N05, 34L05, 35P05, 35L45, 46E35,47A05, 47B36, 81T08, 81Q10, 93E03.

Photographs in preface courtesy of Gerald Teschl and F. Gesztesy, respectively.

Library of Congress Cataloging-in-Publication Data

Spectral analysis, differential equations and mathematical physics : a festschrift in honor of FritzGesztesy’s 60th birthday / Helge Holden, Barry Simon, Gerald Teschl, editors.

p. cm – (Proceedings of symposia in pure mathematics ; volume 87)Includes bibliographical references.ISBN 978-0-8218-7574-2 (alk. paper)1. Differential equations. 2. Mathematical physics. I. Gesztesy, Fritz, 1953– honouree. II.

Holden, H. (Helge), 1956– editor of compilation. III. Simon, Barry, 1946– editor of compilation.IV. Teschl, Gerald, 1970– editor of compilation.

QC20.7.D47S64 2013510–dc23 2012002392

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Contents

Preface v

A mathematical descendants list ix

Publications of Friedrich (Fritz) Gesztesy xi

Invariant measures for stochastic differential equations on networksSergio Albeverio, Luca Di Persio, and Elisa Mastrogiacomo 1

On the spectra of large sparse graphs with cyclesD. Bolle, F. L. Metz, and I. Neri 35

Jones’ extension operator on Sobolev spaces with partially vanishing tracesKevin Brewster, Dorina Mitrea, Irina Mitrea,

and Marius Mitrea 59

Some spectral properties of rooms and passages domains and their skeletonsB. M. Brown, W. D. Evans, and I. G. Wood 69

Finite gap Jacobi matrices: A reviewJacob S. Christiansen, Barry Simon, and Maxim Zinchenko 87

Momentum operators on graphsPavel Exner 105

Asymptotic parabolicity for strongly damped wave equationsGenni Fragnelli, Gisele Ruiz Goldstein, Jerome A. Goldstein,

and Silvia Romanelli 119

On rates in Euler’s formula for C0-semigroupsAlexander Gomilko and Yuri Tomilov 133

Construction of a Noncommutative Quantum Field TheoryHarald Grosse and Raimar Wulkenhaar 153

Periodic conservative solutions for the two-component Camassa–Holm systemKatrin Grunert, Helge Holden, and Xavier Raynaud 165

A minimal uncertainty product for one dimensional semiclassical wave packetsGeorge A. Hagedorn 183

On a transformation of Bohl and its discrete analogueEvans M. Harrell II and Manwah Lilian Wong 191

iii

iv CONTENTS

The Morse and Maslov indices for matrix Hill’s equationsChristopher K. R. T. Jones, Yuri Latushkin,

and Robert Marangell 205

1–D Schrodinger operators with local point interactions: a reviewAleksey Kostenko and Mark Malamud 235

Inverse problem for small oscillationsYu. I. Lyubarskii and V. A. Marchenko 263

On the Weyl-Titchmarsh and Livsic functionsK. A. Makarov and E. Tsekanovskiı 291

Stability for the inverse resonance problem for the CMV operatorRoman Shterenberg, Rudi Weikard, and Maxim Zinchenko 315

On a conjecture of A. BikchentaevF. A. Sukochev 327

Spectral theory as influenced by Fritz GesztesyGerald Teschl and Karl Unterkofler 341

Prescribed asymptotic behavior for nonlinear second-order dynamic equationsMehmet Unal and Agacık Zafer 365

Preface

A room without books is like a body without a soul.

— Attributed to Cicero (106 BC – 43 BC)

Fritz (Friedrich) was born to parents Friederike and Franz Gesztesy on November 5,1953, in Leibnitz, Austria. He was raised there together with his younger sister,Doris.

Fritz attended the local Realgymnasium from 1964 to 1972 and, soon afterthe age of twelve, developed his passion for physics and mathematics. From thisperiod onwards, he spent large parts of his free time, on one hand, in his electronicsworkshop (repairing and reassembling vacuum tube radios and TVs, just before thetransistor revolution took place) and, on the other hand, studying B. Baule’s seven-volume textbook “Die Mathematik des Naturforschers und Ingenieurs”, known as“Der Baule” (developed at the Technical University of Graz, Austria).

Erwin Schodinger Institute, Vienna, July 2011.

Given his strong interests in physics and mathematics, the study of TheoreticalPhysics seemed the most natural choice to him and so he enrolled at the Univer-sity of Graz in the fall of 1972. After studying seven semesters, he presented hisdissertation on a topic in quantum field theory in early 1976. His Ph.D. advisorswere Heimo Latal (University of Graz) and Ludwig Streit (University of Bielefeld,

v

vi PREFACE

Germany). At this point he had become disillusioned with Theoretical Physics perse. Strongly influenced by the monograph of T. Kato and the four-volume treatiseby M. Reed and B. Simon, and especially under the guiding influence of LudwigPittner (University of Graz), Harald Grosse and Walter Thirring (both at the Uni-versity of Vienna), and the four-volume course on Mathematical Physics by thelatter, Fritz decided to devote his future energies to areas in Mathematical Physics.

Fritz was an instructor at the Institute of Theoretical Physics of the Universityof Graz from 1975, became Assistant Professor there in 1977, and Associate Profes-sor (Docent) in 1982, a position he held until 1988, with several interruptions: Theacademic years 1980–81 and 1983–84 were spent at the University of Bielefeld as anAlexander von Humboldt fellow. Around 1986 the idea of a possible switch of con-tinents was raised in conversations with Evans Harrell (Georgia Tech, Atlanta), andthis idea slowly, but steadily, took more concrete form. After a Max Kade fellowshipfor the academic year 1987–88 at the California Institute of Technology, Pasadena,he assumed the position of Full Professor at the Department of Mathematics at theUniversity of Missouri, Columbia, in the fall of 1988, his current affiliation. From2002 he has held the M. & R. Houchins Distinguished Professorship.

Just a few days before his move to Columbia, Missouri, Fritz and Gloria Benoitwere married in Bakersfield, California, in August 1988.

Fritz and Gloria on Maui, Hawaii, June 2008.

Fritz credits Ludwig Streit (Bielefeld), Sergio Albeverio (Bochum and Bonn),Raphael Høegh-Krohn (Oslo), and especially Barry Simon (Caltech) as having hadthe most influence on him over the years. In addition to his two years at Bielefeldand the year at Caltech, he spent time at various research institutions, includingLeuven; CNRS, Luminy, Marseille; LPTHE, Orsay; BiBoS, Bielefeld; IMA, Min-neapolis, Minnesota; CCM, Madeira; University of Vienna; Center for Advanced

PREFACE vii

Study (CAS) at the Norwegian Academy of Science and Letters. Fritz spent manysummer months since 1990 collaborating with Helge Holden at the Norwegian Uni-versity of Science and Technology, Trondheim, Norway, and with Barry Simon atCaltech.

Fritz has received a number of honors, including the Theodor Korner Award inthe Natural Sciences, Vienna (1983), the Ludwig Boltzmann Award of the AustrianPhysical Society (1987), and election to the Royal Norwegian Society of Sciencesand Letters, Trondheim, Norway (2002). He was elected Fellow of the AmericanMathematical Society, inaugural class of 2013.

He has supervised or co-supervised three Ph.D. students at the University ofGraz, one at the Technical University of Graz, one at the University of Louvain-La-Neuve, and nine at the University of Missouri. He takes great pride in the factthat some have become very successful in their own careers and now have successfulstudents of their own. According to the Mathematics Genealogy Project, Fritz has26 mathematical descendants.

Fritz’s editorial responsibilities have included Mathematische Nachrichten, Jour-nal of Mathematical Analysis and Applications, Operators and Matrices, and Jour-nal of Spectral Theory.

Fritz’s research interests developed from spectral and scattering theory forSchrodinger and Dirac-type operators in his early years until about 1988, to in-tegrable systems and their connections with spectral theory (via trace formulas,etc.) from about 1988 to 2006. Since then his interests have primarily returnedto various aspects of spectral theory for elliptic partial differential operators ofrelevance in mathematical physics.

Fritz is an exceptionally generous collaborator, sharing ideas and never sayingno to immense calculations. He prefers to write the final version of the paper him-self, securing precise statements, consistent notation and accurate bibliographies.No reference is too obscure to be checked carefully! Thus, it is no surprise thatFritz at the time this was written, has 95 co-authors and he lists over 240 publica-tions. The author citation data base of MathSciNet shows that Fritz is cited 2295times by 917 authors. His 1988 Springer monograph “Solvable Models in QuantumMechanics”, written jointly with S. Albeverio, R. Høegh-Krohn, and H. Holden,was translated into Russian and appeared with Mir Publishers in 1991. Its sec-ond edition, supplemented with an appendix by P. Exner, appeared in 2005 in theAMS-Chelsea series. It continues to be the authoritative treatise on solvable pointinteraction models and to this day remains an inspiration for research in this area.

As an avid collector of books (his personal library has approximately 5000 ti-tles), Fritz preferred to have a volume of mathematical contributions instead of aconference in his honor. “Books are for life,” he likes to say. Hence, this collection isprimarily devoted to contributions in areas dear to his heart: Spectral Theory, Dif-ferential Equations, and Mathematical Physics. We are grateful to Sergei Gelfand,

viii PREFACE

Christine Thivierge, and the staff at AMS for their support throughout the prepa-rations of this volume. We also thank all the authors for their contributions andthe referees for their invaluable assistance.

Happy Birthday, Fritz!

Helge HoldenBarry SimonGerald Teschl

January, 2013

A mathematical descendants list

Fritz, Universitat Graz, 1976

Vladimir Batchenko, University of Missouri - Columbia, 2005

Ronald Dickson, University of Missouri - Columbia, 1998

Georg Karner, Universitat Graz, 1986

Miroslaw Mystkowski, University of Missouri - Columbia, 1997

Charlotte Nessmann, Universitat Graz, 1984

Manfred Perusch, Universitat Graz, 1982

Ratnam Ratnaseelan, University of Missouri - Columbia, 1996

Walter Renger, University of Missouri - Columbia, 1996

Juma Shabani, Universite Catholique de Louvain, 1986

Mathias Hounkpe, Universite d’Abomey-Calavi, 1996

Alfred Vyabandi, Universite d’Abomey-Calavi, 2001

Wilhelm Sticka, University of Missouri - Columbia, 1995

Gerald Teschl, University of Missouri - Columbia, 1995

Kerstin Ammann, Universitat Wien, 2013

Jonathan Eckhardt, Universitat Wien, 2012

Katrin Grunert, Universitat Wien, 2010

Johanna Michor, Universitat Wien, 2005

Alice Mikikits-Leitner, Universitat Wien, 2009

Mehmet Unal, University of Missouri - Columbia, 1995

Karl Unterkofler, Technische Universitat Graz, 1989

Julian King, Universitat Innsbruck, 2010

Helin Koc Rauchenwald, Universitat Wien, 2011

Klaus Rheinberger, Universitat Innsbruck, 2006

Konrad Schwarz, Universitat Innsbruck, 2009

Robert Tratnig, Technische Universitat Graz, 2005

Maxim Zinchenko, University of Missouri - Columbia, 2006

The most current information can be found at:http://genealogy.math.ndsu.nodak.edu/id.php?id=11336

ix

Publications of Friedrich (Fritz) Gesztesy1

[1]

1976:

“Energiedichten und Renormierung im Modell einer Feldtheorie mitquadratischer Wechselwirkung”. Dissertation, University of Graz, Austria,1976.

[2] F. Gesztesy and H. G. Latal, Renormalization, Nelson’s symmetry and en-ergy densities in a field theory with quadratic interaction, Rep. Math. Phys.14 (1978), no. 2, 215–224, DOI 10.1016/0034-4877(78)90044-7. MR527600(80e:81077)

[3] F. Gesztesy and L. Pittner, Electrons in logarithmic potentials. I. Solution ofthe Schrodinger equation, J. Phys. A 11 (1978), no. 4, 679–686. MR0475458(57 #15064a)

[4] F. Gesztesy and L. Pittner, Electrons in logarithmic potentials. II. Solutionof the Dirac equation, J. Phys. A 11 (1978), no. 4, 687–695. MR0475459(57 #15064b)

[5] F. Gesztesy and L. Pittner, On the commutation relation [A, B] = −icI, Lett.Nuovo Cimento (2) 22 (1978), no. 8, 332–335. MR502163 (82d:81059)

[6] F. Gesztesy and L. Pittner, Uncertainty relations and quadratic forms, J.Phys. A 11 (1978), no. 9, 1765–1770. MR506828 (81a:81028)

[7] F. Gesztesy and L. Pittner, On the Friedrichs extension of ordinary differ-ential operators with strongly singular potentials, Acta Phys. Austriaca 51(1979), no. 3-4, 259–268. MR553603 (81j:47035)

[8] F. Gesztesy and L. Pittner, Diffraction of non-relativistic electron waves bya cylindrical capacitor, J. Phys. A 12 (1979), no. 7, 1091–1104. MR534257(80d:78005)

[9]

1978:

“Diffraction of relativistic electron waves by a cylindrical capacitor”; with L.Pittner. J. Phys. A 12, 2247–2254 (1979).

[10] W. Becker, F. Gesztesy, and H. Mitter, On systems of periodic dif-ferential equations, Lett. Math. Phys. 3 (1979), no. 4, 249–253, DOI10.1007/BF01821842. MR545400 (81m:34063)

[11] F. Gesztesy and L. Pittner, A generalization of the virial theorem for stronglysingular potentials, Rep. Math. Phys. 18 (1980), no. 2, 149–162 (1983), DOI10.1016/0034-4877(80)90082-8. MR730744 (85e:81022)

1Updated: January 4, 2013

xi

xii PUBLICATIONS OF FRITZ

[12] F. Gesztesy, On the one-dimensional Coulomb Hamiltonian, J. Phys. A 13(1980), no. 3, 867–875. MR560542 (80m:81023)

[13] “An efficient method for the summation of partial wave amplitudes for long-range potentials”; with C. B. Lang. Phys. Lett. 79A, 295–297 (1980).

[14] F. Gesztesy, W. Plessas, and B. Thaller, On the high-energy behaviour ofscattering phase shifts for Coulomb-like potentials, J. Phys. A 13 (1980), no. 8,2659–2671. MR582916 (81k:81083)

[15] F. Gesztesy and C. B. Lang, On the Abel summability of partial wave ampli-tudes for Coulomb-type interactions, J. Math. Phys. 22 (1981), no. 2, 312–319,DOI 10.1063/1.524880. MR609622 (83f:40003)

[16] F. Gesztesy and B. Thaller, Born expansions for Coulomb-type interactions,J. Phys. A 14 (1981), no. 3, 639–657. MR605262 (83d:81088)

[17] “A note on quasiperiodic states”; with H. Mitter. J. Phys. A14, L79–L83(1981).

[18] “On the universal low energy limit in nonrelativistic scattering theory”; withS. Albeverio and R. Høegh-Krohn. Acta Phys. Austriaca Suppl. 23, 577–585(1981).

[19] F. Gesztesy, On the structure of Coulomb-type scattering amplitudes, J. Math.Phys. 23 (1982), no. 1, 74–82, DOI 10.1063/1.525209. MR640373 (83c:81103)

[20] S. Albeverio, F. Gesztesy, and R. Høegh-Krohn, The low energy expansionin nonrelativistic scattering theory, Ann. Inst. H. Poincare Sect. A (N.S.) 37(1982), no. 1, 1–28 (English, with French summary). MR667880 (83k:81093)

[21]

1982:

“Spectral concentration in the nonrelativistic limit”; with H. Grosse and B.Thaller. Phys. Lett. 116B, 155–157 (1982).

[22] E. Bruning and F. Gesztesy, Continuity of wave and scattering operatorswith respect to interactions, J. Math. Phys. 24 (1983), no. 6, 1516–1528, DOI10.1063/1.525890. MR708672 (85g:81179)

[23] D. Bolle, F. Gesztesy, and H. Grosse, Time delay for long-range interac-tions, J. Math. Phys. 24 (1983), no. 6, 1529–1541, DOI 10.1063/1.525891.MR708673 (85c:81041)

[24] S. Albeverio, F. Gesztesy, R. Høegh-Krohn, and L. Streit, Charged particleswith short range interactions, Ann. Inst. H. Poincare Sect. A (N.S.) 38 (1983),no. 3, 263–293 (English, with French summary). MR708965 (84j:81107)

[25] S. Albeverio, D. Bolle, F. Gesztesy, and R. Høegh-Krohn, Low-energy pa-rameters in nonrelativistic scattering theory, Ann. Physics 148 (1983), no. 2,308–326, DOI 10.1016/0003-4916(83)90242-7. MR714194 (84j:81108)

[26]

1983:

“Efficient method for calculating relativistic corrections for spin-1/2 parti-cles”; with H. Grosse and B. Thaller. Phys. Rev. Lett. 50, 625–628 (1983).

[27] D. Bolle and F. Gesztesy, On averaged angular time delay for two-body scat-tering, Helv. Phys. Acta 56 (1983), no. 5, 1064–1069. MR728114 (85e:81114)

[28] D. Bolle, F. Gesztesy, and S. F. J. Wilk, New results for scattering on the line,Phys. Lett. A 97 (1983), no. 1-2, 30–34, DOI 10.1016/0375-9601(83)90094-4.MR720677 (85h:81067)

PUBLICATIONS OF FRITZ xiii

[29] “On non-degenerate ground states for Schrodinger operators”. Rep. Math.Phys. 20, 93–109 (1984).

[30] F. Gesztesy and L. Pittner, Two-body scattering for Schrodinger operatorsinvolving zero-range interactions, Rep. Math. Phys. 19 (1984), no. 2, 143–154, DOI 10.1016/0034-4877(84)90012-0. MR740351 (86d:81075)

[31] S. Albeverio, L. S. Ferreira, F. Gesztesy, R. Høegh-Krohn, and L. Streit,Model dependence of Coulomb-corrected scattering lengths, Phys. Rev. C(3) 29 (1984), no. 2, 680–683, DOI 10.1103/PhysRevC.29.680. MR734284(85b:81236)

[32] S. Albeverio, F. Gesztesy, R. Høegh-Krohn, and W. Kirsch, On point inter-actions in one dimension, J. Operator Theory 12 (1984), no. 1, 101–126.MR757115 (86e:81037)

[33] F. Gesztesy, H. Grosse, and B. Thaller, A rigorous approach to relativisticcorrections of bound state energies for spin-12 particles, Ann. Inst. H. PoincarePhys. Theor. 40 (1984), no. 2, 159–174 (English, with French summary).MR747200 (86m:81042)

[34] “On relativistic corrections to bound state energies for two-fermion systems”;with H. Grosse and B. Thaller. Phys. Rev. D30, 2189–2193 (1984).

[35] “Low-energy parametrization of scattering observables in n-dimensional quan-tum systems”; with D. Bolle. Phys. Rev. Lett. 52, 1469–1472 (1984).

[36] S. Albeverio, R. Høegh-Krohn, F. Gesztesy, and H. Holden, Some exactlysolvable models in quantum mechanics and the low energy expansions, Pro-ceedings of the second international conference on operator algebras, ideals,and their applications in theoretical physics (Leipzig, 1983), Teubner-TexteMath., vol. 67, Teubner, Leipzig, 1984, pp. 12–28. MR763518 (85i:81015)

[37] “Scattering observables in arbitrary dimension n ≥ 2”; with D. Bolle. Phys.Rev. A30, 1279–1293 (1984).

[38] F. Gesztesy, Perturbation theory for resonances in terms of Fredholm determi-nants, Resonances—models and phenomena (Bielefeld, 1984), Lecture Notesin Phys., vol. 211, Springer, Berlin, 1984, pp. 78–104, DOI 10.1007/3-540-13880-3 67. MR777333 (86f:81145)

[39] “Scattering lengths in nonrelativistic three-body systems”; with G. Karner.In Few-Body Problems in Physics, Vol. II, B. Zeitnitz (ed.), Elsevier SciencePublishers B. V., 1984, pp. 375–376.

[40] F. Gesztesy, H. Grosse, and B. Thaller, First-order relativistic correctionsand spectral concentration, Adv. in Appl. Math. 6 (1985), no. 2, 159–176,DOI 10.1016/0196-8858(85)90009-0. MR789851 (86j:81026)

[41] D. Bolle, F. Gesztesy, and S. F. J. Wilk, A complete treatment of low-energyscattering in one dimension, J. Operator Theory 13 (1985), no. 1, 3–31.MR768299 (86f:34047)

[42] F. Gesztesy, H. Mitter, and M. Perusch, Scattering theory for time-dependentHamiltonians asymptotically constant in time, J. Math. Anal. Appl. 110(1985), no. 1, 265–282, DOI 10.1016/0022-247X(85)90349-X. MR803434(86i:35114)

[43] F. Gesztesy and W. Kirsch, One-dimensional Schrodinger operators with in-teractions singular on a discrete set, J. Reine Angew. Math. 362 (1985),28–50. MR809964 (87e:34034)

xiv PUBLICATIONS OF FRITZ

[44]

1985:

“On the self-adjointness of Dirac operators with anomalous magnetic mo-ment”; with B. Simon and B. Thaller. Proc. Amer. Math. Soc. 94, 115–118(1985).

[45] S. Albeverio, F. Gesztesy, W. Karwowski, and L. Streit, On the connectionbetween Schrodinger and Dirichlet forms, J. Math. Phys. 26 (1985), no. 10,2546–2553, DOI 10.1063/1.526771. MR803798 (87c:81041)

[46] D. Bolle, F. Gesztesy, and W. Schweiger, Scattering theory for long-rangesystems at threshold, J. Math. Phys. 26 (1985), no. 7, 1661–1674, DOI10.1063/1.526963. MR793308 (87a:81145)

[47] S. Albeverio, Ph. Blanchard, F. Gesztesy, and L. Streit, Quantum mechanicallow energy scattering in terms of diffusion processes, Stochastic aspects ofclassical and quantum systems (Marseille, 1983), Lecture Notes in Math.,vol. 1109, Springer, Berlin, 1985, pp. 207–227, DOI 10.1007/BFb0101546.MR805999 (87c:81164)

[48] “On essential spectra of hard core type Schrodinger operators”; with E.Bruning. J. Phys. A18, L7–L11 (1985).

[49] W. Bulla and F. Gesztesy, Deficiency indices and singular boundary condi-tions in quantum mechanics, J. Math. Phys. 26 (1985), no. 10, 2520–2528,DOI 10.1063/1.526768. MR803795 (87d:35097)

[50] “An exactly solvable periodic Schrodinger operator”; with C. Macedo and L.Streit. J. Phys. A18, L503–L507 (1985).

[51]

1986:

“Threshold behavior and Levinson’s theorem for two-dimensional scatteringsystems: A surprise”; with D. Bolle, C. Danneels, and S. F. J. Wilk. Phys.Rev. Lett. 56, 900–903 (1986).

[52] D. Bolle, F. Gesztesy, C. Nessmann, and L. Streit, Scattering theoryfor general, nonlocal interactions: threshold behavior and sum rules, Rep.Math. Phys. 23 (1986), no. 3, 373–408, DOI 10.1016/0034-4877(86)90032-7.MR913481 (88m:81131)

[53] “Scattering observables in arbitrary dimensions n ≥ 2: An Addendum”; withD. Bolle. Phys. Rev. A33, 3517–3518 (1986).

[54] F. Gesztesy, Scattering theory for one-dimensional systems with non-trivial spatial asymptotics, Schrodinger operators, Aarhus 1985, LectureNotes in Math., vol. 1218, Springer, Berlin, 1986, pp. 93–122, DOI10.1007/BFb0073045. MR869597 (88a:81197)

[55] S. Albeverio, F. Gesztesy, R. Høegh-Krohn, H. Holden, and W. Kirsch, TheSchrodinger operator for a particle in a solid with deterministic and stochas-tic point interactions, Schrodinger operators, Aarhus 1985, Lecture Notes inMath., vol. 1218, Springer, Berlin, 1986, pp. 1–38, DOI 10.1007/BFb0073042.MR869594 (88a:81030)

[56] F. Gesztesy, G. Karner, and L. Streit, Charged particles with a short-rangeforce: perturbation theory with respect to the range and to additional effects,J. Math. Phys. 27 (1986), no. 1, 249–261, DOI 10.1063/1.527369. MR816440(87g:81118)

PUBLICATIONS OF FRITZ xv

[57] F. Gesztesy and H. Holden, A unified approach to eigenvalues and resonancesof Schrodinger operators using Fredholm determinants, J. Math. Anal. Appl.123 (1987), no. 1, 181–198, DOI 10.1016/0022-247X(87)90303-9. MR881540(88c:35117)

[58] D. Bolle, F. Gesztesy, and M. Klaus, Scattering theory for one-dimensionalsystems with

∫dx V (x) = 0, J. Math. Anal. Appl. 122 (1987), no. 2, 496–518,

DOI 10.1016/0022-247X(87)90281-2. MR877834 (89k:34028a)[59] F. Gesztesy and G. Karner, On three-body scattering near thresholds, SIAM J.

Math. Anal. 18 (1987), no. 4, 1064–1086, DOI 10.1137/0518079. MR892489(88j:81076)

[60] “Point interactions in two dimensions. Basic properties and applications tosolid state physics”; with S. Albeverio, R. Høegh-Krohn, and H. Holden. J.reine angew. Math. 308, 87–107 (1987).

[61] D. Bolle, F. Gesztesy, H. Grosse, and B. Simon, Kreın’s spectral shift func-tion and Fredholm determinants as efficient methods to study supersymmet-ric quantum mechanics, Lett. Math. Phys. 13 (1987), no. 2, 127–133, DOI10.1007/BF00955200. MR886147 (88f:81043)

[62] D. Bolle, F. Gesztesy, H. Grosse, W. Schweiger, and B. Simon, Wittenindex, axial anomaly, and Kreın’s spectral shift function in supersymmet-ric quantum mechanics, J. Math. Phys. 28 (1987), no. 7, 1512–1525, DOI10.1063/1.527508. MR894842 (88j:81022)

[63] E. Bruning, M. Demuth, and F. Gesztesy, Invariance of the essential spectrafor perturbations with unbounded hard cores, Lett. Math. Phys. 13 (1987),no. 1, 69–77, DOI 10.1007/BF00570770. MR878664 (88c:35115)

[64] J.-P. Antoine, F. Gesztesy, and J. Shabani, Exactly solvable models of sphereinteractions in quantum mechanics, J. Phys. A 20 (1987), no. 12, 3687–3712.MR913638 (89d:81027)

[65] F. Gesztesy and P. Seba, New analytically solvable models of relativis-tic point interactions, Lett. Math. Phys. 13 (1987), no. 4, 345–358, DOI10.1007/BF00401163. MR895297 (89b:81034)

[66] F. Gesztesy and H. Holden, A new class of solvable models in quantum me-chanics describing point interactions on the line, J. Phys. A 20 (1987), no. 15,5157–5177. MR914699 (89a:81016)

[67] F. Gesztesy, On stationary two-body scattering theory in two dimensions,Models and methods in few-body physics (Lisbon, 1986), Lecture Notes inPhys., vol. 273, Springer, Berlin, 1987, pp. 609–629, DOI 10.1007/3-540-17647-0 42. MR899147

[68] F. Gesztesy, H. Holden, and W. Kirsch, On energy gaps in a new typeof analytically solvable model in quantum mechanics, J. Math. Anal. Appl.134 (1988), no. 1, 9–29, DOI 10.1016/0022-247X(88)90003-0. MR958850(90c:81032)

[69] F. Gesztesy and B. Simon, Topological invariance of the Witten index, J.Funct. Anal. 79 (1988), no. 1, 91–102, DOI 10.1016/0022-1236(88)90031-6.MR950085 (90a:47032)

[70] D. Bolle, F. Gesztesy, and C. Danneels, Threshold scattering in two dimen-sions, Ann. Inst. H. Poincare Phys. Theor. 48 (1988), no. 2, 175–204 (English,with French summary). MR952661 (89k:81184)

xvi PUBLICATIONS OF FRITZ

[71] W. Bulla, F. Gesztesy, and K. Unterkofler, On relativistic energy band cor-rections in the presence of periodic potentials, Lett. Math. Phys. 15 (1988),no. 4, 313–324, DOI 10.1007/BF00419589. MR952454 (90c:81038)

[72] F. Gesztesy and B. Simon, On a theorem of Deift and Hempel, Comm. Math.Phys. 116 (1988), no. 3, 503–505. MR937772 (89g:35080)

[73] F. Gesztesy, D. Gurarie, H. Holden, M. Klaus, L. Sadun, B. Simon, and P.Vogl, Trapping and cascading of eigenvalues in the large coupling limit, Comm.Math. Phys. 118 (1988), no. 4, 597–634. MR962490 (89m:81049)

[74] S. Albeverio, R. Figari, F. Gesztesy, R. Høegh-Krohn, H. Holden, and W.Kirsch, Point interaction Hamiltonians for crystals with random defects,Applications of selfadjoint extensions in quantum physics (Dubna, 1987),Lecture Notes in Phys., vol. 324, Springer, Berlin, 1989, pp. 87–99, DOI10.1007/BFb0022960. MR1009843

[75] F. Gesztesy, H. Holden, and P. Seba, On point interactions in magnetic fieldsystems, Schrodinger operators, standard and nonstandard (Dubna, 1988),World Sci. Publ., Teaneck, NJ, 1989, pp. 146–164. MR1091996 (91m:81044)

[76] F. Gesztesy, Some applications of commutation methods, Schrodinger opera-tors (Sønderborg, 1988), Lecture Notes in Phys., vol. 345, Springer, Berlin,1989, pp. 93–117, DOI 10.1007/3-540-51783-9 18. MR1037318 (91g:58246)

[77] F. Gesztesy and B. Simon, Constructing solutions of the mKdV-equation, J.Funct. Anal. 89 (1990), no. 1, 53–60, DOI 10.1016/0022-1236(90)90003-4.MR1040955 (91e:35183)

[78] F. Gesztesy, W. Schweiger, and B. Simon, Commutation methods applied tothe mKdV-equation, Trans. Amer. Math. Soc. 324 (1991), no. 2, 465–525,DOI 10.2307/2001730. MR1029000 (92b:35132)

[79] F. Gesztesy and Z. Zhao, On critical and subcritical Sturm-Liouville operators,J. Funct. Anal. 98 (1991), no. 2, 311–345, DOI 10.1016/0022-1236(91)90081-F. MR1111572 (93f:34146)

[80] F. Gesztesy, H. Holden, E. Saab, and B. Simon, Explicit construction ofsolutions of the modified Kadomtsev-Petviashvili equation, J. Funct. Anal.98 (1991), no. 1, 211–228, DOI 10.1016/0022-1236(91)90096-N. MR1111199(92h:35206)

[81] F. Gesztesy, On the modified Korteweg-de Vries equation, engineering(Leibnitz, 1989), Lecture Notes in Pure and Appl. Math., vol. 133, Dekker,New York, 1991, pp. 139–183. MR1171468 (93i:35123)

[82] F. Gesztesy and W. Schweiger, Rational KP and mKP-solutions in Wronskianform, Rep. Math. Phys. 30 (1991), no. 2, 205–222 (1992), DOI 10.1016/0034-4877(91)90025-I. MR1188396 (94a:58089)

[83] F. Gesztesy, (m)KdV-soliton solutions on quasi-periodic finite-gap back-grounds, Nonlinear fields: classical, random, semiclassical (Karpacz, 1991),World Sci. Publ., River Edge, NJ, 1991, pp. 171–194. MR1146003 (93e:58082)

[84] W. Bulla, F. Gesztesy, and K. Unterkofler, Holomorphy of the scatteringmatrix with respect to c−2 for Dirac operators and an explicit treatmentof relativistic corrections, Comm. Math. Phys. 144 (1992), no. 2, 391–416.MR1152379 (93b:81302)

[85] F. Gesztesy, Quasi-periodic, finite-gap solutions of the modified Korteweg-deVries equation, applications (Oslo, 1988), Cambridge Univ. Press, Cambridge,1992, pp. 428–471. MR1190516 (94d:35144)

PUBLICATIONS OF FRITZ xvii

[86] F. Gesztesy and H. Holden, A new representation of soliton solutions of theKadomtsev-Petviashvili equation, applications (Oslo, 1988), Cambridge Univ.Press, Cambridge, 1992, pp. 472–479. MR1190517 (93i:35124)

[87] F. Gesztesy and K. Unterkofler, Isospectral deformations for Sturm-Liouvilleand Dirac-type operators and associated nonlinear evolution equations, Rep.Math. Phys. 31 (1992), no. 2, 113–137, DOI 10.1016/0034-4877(92)90008-O.MR1227036 (94f:35124)

[88] F. Gesztesy, W. Karwowski, and Z. Zhao, New types of soliton solutions, Bull.Amer. Math. Soc. (N.S.) 27 (1992), no. 2, 266–272, DOI 10.1090/S0273-0979-1992-00309-9. MR1152159 (93c:35138)

[89] F. Gesztesy, W. Karwowski, and Z. Zhao, Limits of soliton solutions, DukeMath. J. 68 (1992), no. 1, 101–150, DOI 10.1215/S0012-7094-92-06805-0.MR1185820 (94b:35242)

[90] F. Gesztesy, G. M. Graf, and B. Simon, The ground state energy ofSchrodinger operators, Comm. Math. Phys. 150 (1992), no. 2, 375–384.MR1194022 (93j:47070)

[91] F. Gesztesy and Z. Zhao, Critical and subcritical Jacobi operators defined asFriedrichs extensions, J. Differential Equations 103 (1993), no. 1, 68–93, DOI10.1006/jdeq.1993.1042. MR1218739 (94m:47065)

[92] F. Gesztesy, H. Holden, B. Simon, and Z. Zhao, On the Toda and Kac-vanMoerbeke systems, Trans. Amer. Math. Soc. 339 (1993), no. 2, 849–868, DOI10.2307/2154302. MR1153014 (93m:58050)

[93] F. Gesztesy and B. Simon, A short proof of Zheludev’s theorem, Trans. Amer.Math. Soc. 335 (1993), no. 1, 329–340, DOI 10.2307/2154271. MR1096260(93c:34162)

[94] Friedrich Gesztesy, David Race, and Rudi Weikard,On (modified) Boussinesq-type systems and factorizations of associated linear differential expressions,J. London Math. Soc. (2) 47 (1993), no. 2, 321–340, DOI 10.1112/jlms/s2-47.2.321. MR1207952 (95c:35212)

[95] F. Gesztesy and R. Weikard, Spectral deformations and soliton equations,Differential equations with applications to mathematical physics, Math. Sci.Engrg., vol. 192, Academic Press, Boston, MA, 1993, pp. 101–139, DOI10.1016/S0076-5392(08)62376-0. MR1207152 (93m:34138)

[96] F. Gesztesy, A complete spectral characterization of the double com-mutation method, J. Funct. Anal. 117 (1993), no. 2, 401–446, DOI10.1006/jfan.1993.1132. MR1244942 (94m:47093)

[97] F. Gesztesy, H. Holden, B. Simon, and Z. Zhao, Trace formulae and inversespectral theory for Schrodinger operators, Bull. Amer. Math. Soc. (N.S.) 29(1993), no. 2, 250–255, DOI 10.1090/S0273-0979-1993-00431-2. MR1215308(94c:34127)

[98] F. Gesztesy, D. Race, K. Unterkofler, and R. Weikard, On Gelfand-Dickeyand Drinfeld-Sokolov systems, Rev. Math. Phys. 6 (1994), no. 2, 227–276,DOI 10.1142/S0129055X94000122. MR1269299 (95g:58104)

[99] F. Gesztesy and Z. Zhao, Domain perturbations, Brownian motion, capacities,and ground states of Dirichlet Schrodinger operators, Math. Z. 215 (1994),no. 1, 143–150, DOI 10.1007/BF02571703. MR1254817 (95g:60098)

xviii PUBLICATIONS OF FRITZ

[100] F. Gesztesy and H. Holden, Trace formulas and conservation laws for non-linear evolution equations, Rev. Math. Phys. 6 (1994), no. 1, 51–95, DOI10.1142/S0129055X94000055. MR1263198 (95h:35198a)

[101] “New trace formulas for Schrodinger operators”. In Evolution Equations, G.Ferreyra, G. Goldstein, and F. Neubrander (eds.), Marcel Dekker, 1995, pp.201–221.

[102] F. Gesztesy and R. Weikard, Picard and finite-gap potentials, Evolution equa-tions (Baton Rouge, LA, 1992), Lecture Notes in Pure and Appl. Math.,vol. 168, Dekker, New York, 1995, pp. 223–233. MR1300431 (95h:35191)

[103] F. Gesztesy and K. Unterkofler, On the (modified) Kadomtsev-Petviashvili hi-erarchy, Differential Integral Equations 8 (1995), no. 4, 797–812. MR1306592(95h:35199)

[104] F. Gesztesy and Z. Zhao, On positive solutions of critical Schrodinger oper-ators in two dimensions, J. Funct. Anal. 127 (1995), no. 1, 235–256, DOI10.1006/jfan.1995.1010. MR1308624 (96a:35037)

[105] F. Gesztesy and R. Weikard, On Picard potentials, Differential Integral Equa-tions 8 (1995), no. 6, 1453–1476. MR1329850 (96e:34141)

[106] Fritz Gesztesy and Roman Svirsky, (m)KdV solitons on the backgroundof quasi-periodic finite-gap solutions, Mem. Amer. Math. Soc. 118 (1995),no. 563, iv+88. MR1303091 (96c:35162)

[107] F. Gesztesy and R. Weikard, Treibich-Verdier potentials and the sta-tionary (m)KdV hierarchy, Math. Z. 219 (1995), no. 3, 451–476, DOI10.1007/BF02572375. MR1339715 (96e:14030)

[108] F. Gesztesy and B. Simon, Rank-one perturbations at infinite coupling,J. Funct. Anal. 128 (1995), no. 1, 245–252, DOI 10.1006/jfan.1995.1030.MR1317717 (95m:47014)

[109] F. Gesztesy, H. Holden, and B. Simon, Absolute summability of the tracerelation for certain Schrodinger operators, Comm. Math. Phys. 168 (1995),no. 1, 137–161. MR1324393 (96b:34110)

[110] F. Gesztesy and R. Weikard, Lame potentials and the stationary (m)KdVhierarchy, Math. Nachr. 176 (1995), 73–91, DOI 10.1002/mana.19951760107.MR1361127 (98a:58086)

[111] F. Gesztesy, H. Holden, B. Simon, and Z. Zhao, Higher order trace relationsfor Schrodinger operators, Rev. Math. Phys. 7 (1995), no. 6, 893–922, DOI10.1142/S0129055X95000347. MR1348829 (97d:34094)

[112] F. Gesztesy and H. Holden, On new trace formulae for Schrodinger operators,Acta Appl. Math. 39 (1995), no. 1-3, 315–333, DOI 10.1007/BF00994640.KdV ’95 (Amsterdam, 1995). MR1329568 (96f:35126)

[113] M. Demuth, F. Gesztesy, J. van Casteren, and Z. Zhao, Finite capacitiesin spectral theory, Partial differential operators and mathematical physics(Holzhau, 1994), Oper. Theory Adv. Appl., vol. 78, Birkhauser, Basel, 1995,pp. 89–97. MR1365320 (97c:47052)

[114] F. Gesztesy and R. Weikard, Floquet theory revisited, Differential equationsand mathematical physics (Birmingham, AL, 1994), Int. Press, Boston, MA,1995, pp. 67–84. MR1703573 (2000i:34163)

[115] Fritz Gesztesy and Rudi Weikard, A characterization of elliptic finite-gappotentials, C. R. Acad. Sci. Paris Ser. I Math. 321 (1995), no. 7, 837–841(English, with English and French summaries). MR1355838 (96k:58112)

PUBLICATIONS OF FRITZ xix

[116] Fritz Gesztesy and Barry Simon, The xi function, Acta Math. 176 (1996),no. 1, 49–71, DOI 10.1007/BF02547335. MR1395669 (97e:47078)

[117] Fritz Gesztesy and Rudi Weikard, Picard potentials and Hill’s equation ona torus, Acta Math. 176 (1996), no. 1, 73–107, DOI 10.1007/BF02547336.MR1395670 (97f:14046)

[118] F. Gesztesy and G. Teschl, On the double commutation method, Proc. Amer.Math. Soc. 124 (1996), no. 6, 1831–1840, DOI 10.1090/S0002-9939-96-03299-6. MR1322925 (96h:34171)

[119] F. Gesztesy and G. Teschl, Commutation methods for Jacobi operators, J. Dif-ferential Equations 128 (1996), no. 1, 252–299, DOI 10.1006/jdeq.1996.0095.MR1392402 (97i:47079)

[120] F. Gesztesy and B. Simon, Uniqueness theorems in inverse spectral theory forone-dimensional Schrodinger operators, Trans. Amer. Math. Soc. 348 (1996),no. 1, 349–373, DOI 10.1090/S0002-9947-96-01525-5. MR1329533 (96e:34030)

[121] F. Gesztesy, B. Simon, and G. Teschl, Zeros of the Wronskian and renor-malized oscillation theory, Amer. J. Math. 118 (1996), no. 3, 571–594.MR1393260 (97g:34105)

[122] F. Gesztesy, M. Krishna, and G. Teschl, On isospectral sets of Jacobi opera-tors, Comm. Math. Phys. 181 (1996), no. 3, 631–645. MR1414303 (97i:47048)

[123] F. Gesztesy, B. Simon, and G. Teschl, Spectral deformations of one-dimensional Schrodinger operators, J. Anal. Math. 70 (1996), 267–324, DOI10.1007/BF02820446. MR1444263 (98m:34171)

[124] F. Gesztesy, R. Ratnaseelan, and G. Teschl, The KdV hierarchy and associatedtrace formulas, Recent developments in operator theory and its applications(Winnipeg, MB, 1994), Oper. Theory Adv. Appl., vol. 87, Birkhauser, Basel,1996, pp. 125–163. MR1399359 (97m:58095)

[125] F. Gesztesy, H. Holden, B. Simon, and Z. Zhao, A trace formula for multidi-mensional Schrodinger operators, J. Funct. Anal. 141 (1996), no. 2, 449–465,DOI 10.1006/jfan.1996.0137. MR1418515 (97i:47098)

[126] F. Gesztesy and H. Holden, On trace formulas for Schrodinger-type opera-tors, and molecular physics (Minneapolis, MN, 1995), IMA Vol. Math. Appl.,vol. 89, Springer, New York, 1997, pp. 121–145, DOI 10.1007/978-1-4612-1870-8 5. MR1487920 (98m:34172)

[127] W. Bulla, F. Gesztesy, W. Renger, and B. Simon,Weakly coupled bound statesin quantum waveguides, Proc. Amer. Math. Soc. 125 (1997), no. 5, 1487–1495,DOI 10.1090/S0002-9939-97-03726-X. MR1371117 (97g:81009)

[128] F. Gesztesy, R. Nowell, and W. Potz, One-dimensional scattering theoryfor quantum systems with nontrivial spatial asymptotics, Differential IntegralEquations 10 (1997), no. 3, 521–546. MR1744860 (2000k:81392)

[129] F. Gesztesy and W. Renger, New classes of Toda soliton solutions,Comm. Math. Phys. 184 (1997), no. 1, 27–50, DOI 10.1007/s002200050051.MR1462498 (99f:58097)

[130] Fritz Gesztesy and Barry Simon, Inverse spectral analysis with partial in-formation on the potential. I. The case of an a.c. component in the spec-trum, Helv. Phys. Acta 70 (1997), no. 1-2, 66–71. Papers honouring the60th birthday of Klaus Hepp and of Walter Hunziker, Part II (Zurich, 1995).MR1441597 (98f:81347)

xx PUBLICATIONS OF FRITZ

[131] Rafael del Rio, Fritz Gesztesy, and Barry Simon, Inverse spectral anal-ysis with partial information on the potential. III. Updating bound-ary conditions, Internat. Math. Res. Notices 15 (1997), 751–758, DOI10.1155/S1073792897000494. MR1470376 (99a:34032)

[132] Fritz Gesztesy and Barry Simon, m-functions and inverse spectral analysis forfinite and semi-infinite Jacobi matrices, J. Anal. Math. 73 (1997), 267–297,DOI 10.1007/BF02788147. MR1616422 (99c:47039)

[133] F. Gesztesy and M. Unal, Perturbative oscillation criteria andHardy-type inequalities, Math. Nachr. 189 (1998), 121–144, DOI10.1002/mana.19981890108. MR1492926 (99a:34069)

[134] W. Bulla, F. Gesztesy, H. Holden, and G. Teschl, Algebro-geometric quasi-periodic finite-gap solutions of the Toda and Kac-van Moerbeke hierarchies,Mem. Amer. Math. Soc. 135 (1998), no. 641, x+79. MR1432141 (99b:58109)

[135] F. Gesztesy and R. Ratnaseelan, An alternative approach to algebro-geometricsolutions of the AKNS hierarchy, Rev. Math. Phys. 10 (1998), no. 3, 345–391,DOI 10.1142/S0129055X98000112. MR1626836 (99d:58079)

[136] F. Gesztesy and W. Sticka, On a theorem of Picard, Proc. Amer. Math.Soc. 126 (1998), no. 4, 1089–1099, DOI 10.1090/S0002-9939-98-04668-1.MR1476130 (98m:34012)

[137] Fritz Gesztesy and Rudi Weikard, A characterization of all elliptic algebro-geometric solutions of the AKNS hierarchy, Acta Math. 181 (1998), no. 1,63–108, DOI 10.1007/BF02392748. MR1654775 (99k:14052)

[138] Fritz Gesztesy, Konstantin A. Makarov, and Eduard Tsekanovskii, An ad-dendum to Krein’s formula, J. Math. Anal. Appl. 222 (1998), no. 2, 594–606,DOI 10.1006/jmaa.1998.5948. MR1628437 (99g:47047)

[139] Fritz Gesztesy and Rudi Weikard, Elliptic algebro-geometric solutions ofthe KdV and AKNS hierarchies—an analytic approach, Bull. Amer. Math.Soc. (N.S.) 35 (1998), no. 4, 271–317, DOI 10.1090/S0273-0979-98-00765-4.MR1638298 (99i:58075)

[140] F. Gesztesy and R. Weikard, Toward a characterization of elliptic solutions ofhierarchies of soliton equations, Applied analysis (Baton Rouge, LA, 1996),Contemp. Math., vol. 221, Amer. Math. Soc., Providence, RI, 1999, pp. 133–161, DOI 10.1090/conm/221/03120. MR1647205 (99k:58090)

[141] Ronnie Dickson, Fritz Gesztesy, and Karl Unterkofler, A new approachto the Boussinesq hierarchy, Math. Nachr. 198 (1999), 51–108, DOI10.1002/mana.19991980105. MR1670365 (99m:35204)

[142] Fritz Gesztesy and Barry Simon, On the determination of a potential fromthree spectra, Differential operators and spectral theory, Amer. Math. Soc.Transl. Ser. 2, vol. 189, Amer. Math. Soc., Providence, RI, 1999, pp. 85–92.MR1730505 (2000i:34026)

[143] Fritz Gesztesy, Konstantin A. Makarov, and Serguei N. Naboko, The spectralshift operator, Mathematical results in quantum mechanics (Prague, 1998),Oper. Theory Adv. Appl., vol. 108, Birkhauser, Basel, 1999, pp. 59–90.MR1708788 (2000k:47012)

[144] “Corrections and addendum to Inverse spectral analysis with partial informa-tion on the potential, III. Updating boundary conditions”; with R. del Rio andB. Simon. Int. Math. Res. Notices 1999, No. 11, 623–625.

PUBLICATIONS OF FRITZ xxi

[145] R. Dickson, F. Gesztesy, and K. Unterkofler, Algebro-geometric solutions ofthe Boussinesq hierarchy, Rev. Math. Phys. 11 (1999), no. 7, 823–879, DOI10.1142/S0129055X9900026X. MR1702719 (2000d:14040)

[146] Fritz Gesztesy and Barry Simon, Inverse spectral analysis with partial in-formation on the potential. II. The case of discrete spectrum, Trans. Amer.Math. Soc. 352 (2000), no. 6, 2765–2787, DOI 10.1090/S0002-9947-99-02544-1. MR1694291 (2000j:34019)

[147] Fritz Gesztesy and Helge Holden, A combined sine-Gordon and modifiedKorteweg-de Vries hierarchy and its algebro-geometric solutions, Differentialequations and mathematical physics (Birmingham, AL, 1999), AMS/IP Stud.Adv. Math., vol. 16, Amer. Math. Soc., Providence, RI, 2000, pp. 133–173.MR1764748 (2001f:37114)

[148] Fritz Gesztesy and Eduard Tsekanovskii, On matrix-valued Her-glotz functions, Math. Nachr. 218 (2000), 61–138, DOI 10.1002/1522-2616(200010)218:1¡61::AID-MANA61¿3.3.CO;2-4. MR1784638 (2001j:47018)

[149] Steve Clark, Fritz Gesztesy, Helge Holden, and Boris M. Levitan, Borg-type theorems for matrix-valued Schrodinger operators, J. Differential Equa-tions 167 (2000), no. 1, 181–210, DOI 10.1006/jdeq.1999.3758. MR1785118(2002d:34019)

[150] Fritz Gesztesy and Helge Holden, The classical Boussinesq hierarchy revisited,Skr. K. Nor. Vidensk. Selsk. 1 (2000), 15. MR1828737 (2002b:35178)

[151] Fritz Gesztesy and Helge Holden, Darboux-type transformations and hy-perelliptic curves, J. Reine Angew. Math. 527 (2000), 151–183, DOI10.1515/crll.2000.080. MR1794021 (2002b:37108)

[152] Fritz Gesztesy and Konstantin A. Makarov, Some applications of the spec-tral shift operator, Operator theory and its applications (Winnipeg, MB,1998), Fields Inst. Commun., vol. 25, Amer. Math. Soc., Providence, RI, 2000,pp. 267–292. MR1759548 (2001f:47018)

[153] Fritz Gesztesy and Konstantin A. Makarov, The Ξ operator and its relationto Krein’s spectral shift function, J. Anal. Math. 81 (2000), 139–183, DOI10.1007/BF02788988. MR1785280 (2001i:47016)

[154] F. Gesztesy, C. K. R. T. Jones, Y. Latushkin, and M. Stanislavova, Aspectral mapping theorem and invariant manifolds for nonlinear Schrodingerequations, Indiana Univ. Math. J. 49 (2000), no. 1, 221–243, DOI10.1512/iumj.2000.49.1838. MR1777032 (2001g:37144)

[155] “The classical massive Thirring system revisited”; with V. Z. Enolskii and H.Holden. In Stochastic Processes, Physics and Geometry: New Interplays. I.A Volume in Honor of Sergio Albeverio, F. Gesztesy, H. Holden, J. Jost, S.Paycha, M. Rockner, and S. Scarlatti (eds.), Canadian Mathematical SocietyConference Proceedings, Vol. 28, Amer. Math. Soc., Providence, RI, 2000, pp.163–200.

[156] Stochastic processes, physics and geometry: new interplays. II, CMS Confer-ence Proceedings, vol. 29, American Mathematical Society, Providence, RI,2000. A volume in honor of Sergio Albeverio; Edited by Fritz Gesztesy, HelgeHolden, Jurgen Jost, Sylvie Paycha, Michael Rockner and Sergio Scarlatti.MR1803398 (2001f:00037)

xxii PUBLICATIONS OF FRITZ

[157] Fritz Gesztesy and Alexander G. Ramm, An inverse problem for pointinhomogeneities, Methods Funct. Anal. Topology 6 (2000), no. 2, 1–12.MR1783771 (2001h:47032)

[158] Fritz Gesztesy and Barry Simon, On local Borg-Marchenko uniqueness results,Comm. Math. Phys. 211 (2000), no. 2, 273–287, DOI 10.1007/s002200050812.MR1754515 (2001b:34020)

[159] F. Gesztesy, K. Unterkofler, and R. Weikard, On a theorem of Halphen andits application to integrable systems, J. Math. Anal. Appl. 251 (2000), no. 2,504–526, DOI 10.1006/jmaa.2000.7026. MR1794755 (2001i:37108)

[160] Fritz Gesztesy and Helge Holden, The Cole-Hopf and Miura transformationsrevisited, Mathematical physics and stochastic analysis (Lisbon, 1998), WorldSci. Publ., River Edge, NJ, 2000, pp. 198–214. MR1893107 (2003a:37107)

[161] Fritz Gesztesy and Barry Simon, A new approach to inverse spectral theory.II. General real potentials and the connection to the spectral measure, Ann.of Math. (2) 152 (2000), no. 2, 593–643, DOI 10.2307/2661393. MR1804532(2001m:34185b)

[162] Fritz Gesztesy, Integrable systems in the infinite genus limit, Differential In-tegral Equations 14 (2001), no. 6, 671–700. MR1826956 (2002f:37124)

[163] Steve Clark and Fritz Gesztesy,Weyl-Titchmarsh M -function asymptotics formatrix-valued Schrodinger operators, Proc. London Math. Soc. (3) 82 (2001),no. 3, 701–724, DOI 10.1112/plms/82.3.701. MR1816694 (2002c:34144)

[164] Fritz Gesztesy, Nigel J. Kalton, Konstantin A. Makarov, and EduardTsekanovskii, Some applications of operator-valued Herglotz functions, Op-erator theory, system theory and related topics (Beer-Sheva/Rehovot, 1997),Oper. Theory Adv. Appl., vol. 123, Birkhauser, Basel, 2001, pp. 271–321.MR1821917 (2002f:47049)

[165] Fritz Gesztesy and Helge Holden, Dubrovin equations and integrable systemson hyperelliptic curves, Math. Scand. 91 (2002), no. 1, 91–126. MR1917684(2003d:37120)

[166] Fritz Gesztesy, Alexander Kiselev, and Konstantin A. Makarov, Unique-ness results for matrix-valued Schrodinger, Jacobi, and Dirac-type op-erators, Math. Nachr. 239/240 (2002), 103–145, DOI 10.1002/1522-2616(200206)239:1¡103::AID-MANA103¿3.0.CO;2-F. MR1905666(2003i:47047)

[167] Steve Clark and Fritz Gesztesy, Weyl-Titchmarsh M -function asymptotics,local uniqueness results, trace formulas, and Borg-type theorems for Diracoperators, Trans. Amer. Math. Soc. 354 (2002), no. 9, 3475–3534 (electronic),DOI 10.1090/S0002-9947-02-03025-8. MR1911509 (2003i:34191)

[168] Fritz Gesztesy and Helge Holden, Algebro-geometric solutions of the Camassa-Holm hierarchy, Rev. Mat. Iberoamericana 19 (2003), no. 1, 73–142, DOI10.4171/RMI/339. MR1993416 (2004e:37113)

[169] Fritz Gesztesy and Lev A. Sakhnovich, A class of matrix-valued Schrodingeroperators with prescribed finite-band spectra, Reproducing kernel spaces andapplications, Oper. Theory Adv. Appl., vol. 143, Birkhauser, Basel, 2003,pp. 213–253. MR2019352 (2005g:47091)

[170] Eugene D. Belokolos, Fritz Gesztesy, Konstantin A. Makarov, and LevA. Sakhnovich, Matrix-valued generalizations of the theorems of Borg and

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Hochstadt, Evolution equations, Lecture Notes in Pure and Appl. Math.,vol. 234, Dekker, New York, 2003, pp. 1–34. MR2073733 (2005j:47046)

[171] Steve Clark and Fritz Gesztesy, On Povzner-Wienholtz-type self-adjointnessresults for matrix-valued Sturm-Liouville operators, Proc. Roy. Soc. Edin-burgh Sect. A 133 (2003), no. 4, 747–758, DOI 10.1017/S0308210500002651.MR2006200 (2004h:47067)

[172] Fritz Gesztesy and Konstantin A. Makarov, (Modified) Fredholm determi-nants for operators with matrix-valued semi-separable integral kernels revis-ited, Integral Equations Operator Theory 47 (2003), no. 4, 457–497, DOI10.1007/s00020-003-1170-y. MR2021969 (2006g:47076)

[173] Vladimir Batchenko and Fritz Gesztesy, The spectrum of Schrodinger oper-ators with quasi-periodic algebro-geometric KdV potentials, Mat. Fiz. Anal.Geom. 10 (2003), no. 4, 447–468. MR2020819 (2004i:37140)

[174] F. Gestezi and K. A. Makarov, SL2(R), exponential representation of Herglotzfunctions, and spectral averaging, Algebra i Analiz 15 (2003), no. 3, 104–144(Russian, with Russian summary); English transl., St. Petersburg Math. J.15 (2004), no. 3, 393–418. MR2052165 (2006f:47004)

[175] Radu C. Cascaval, Fritz Gesztesy, Helge Holden, and Yuri Latushkin, Spec-tral analysis of Darboux transformations for the focusing NLS hierarchy, J.Anal. Math. 93 (2004), 139–197, DOI 10.1007/BF02789306. MR2110327(2006e:37128)

[176] Steve Clark and Fritz Gesztesy, On Weyl-Titchmarsh theory for singular finitedifference Hamiltonian systems, J. Comput. Appl. Math. 171 (2004), no. 1-2,151–184, DOI 10.1016/j.cam.2004.01.011. MR2077203 (2006i:39033)

[177] Fritz Gesztesy and Barry Simon, Connectedness of the isospectral manifold forone-dimensional half-line Schrodinger operators, J. Statist. Phys. 116 (2004),no. 1-4, 361–365, DOI 10.1023/B:JOSS.0000037217.89500.b3. MR2083146(2005e:81057)

[178] Radu Cascaval and Fritz Gesztesy, I-self-adjointness of a class of Dirac-type operators, J. Math. Anal. Appl. 294 (2004), no. 1, 113–121, DOI10.1016/j.jmaa.2004.02.002. MR2059793 (2005d:47079)

[179] “Algebro-geometric solutions of the KdV and Camassa–Holm equation”; withH. Holden. Oberwolfach Workshop on Wave Motion, A. Constantin and J.Escher (organizers), Oberwolfach Report 5, 275–280 (2004).

[180] “Evans Functions and Modified Fredholm Determinants”; with Y. Latushkinand K. A. Makarov. Oberwolfach Workshop on Spectral Theory in BanachSpaces and Harmonic Analysis, N. Kalton, A. G. R. McIntosh, and L. Weis(organizers), Oberwolfach Report 36, 1950–1953 (2004).

[181] Jeffrey S. Geronimo, Fritz Gesztesy, and Helge Holden, Algebro-geometricsolutions of the Baxter-Szego difference equation, Comm. Math. Phys.258 (2005), no. 1, 149–177, DOI 10.1007/s00220-005-1305-x. MR2166844(2006e:37129)

[182] Volodymyr Batchenko and Fritz Gesztesy, On the spectrum of Schrodingeroperators with quasi-periodic algebro-geometric KdV potentials, J. Anal. Math.95 (2005), 333–387, DOI 10.1007/BF02791507. MR2145569 (2006a:34236)

[183] Steve Clark, Fritz Gesztesy, and Walter Renger, Trace formulas andBorg-type theorems for matrix-valued Jacobi and Dirac finite difference

xxiv PUBLICATIONS OF FRITZ

operators, J. Differential Equations 219 (2005), no. 1, 144–182, DOI10.1016/j.jde.2005.04.013. MR2181033 (2006e:47068)

[184]

2005:

“Non-self-adjoint operators, infinite determinants, and some applications”;with Y. Latushkin, M. Mitrea, and M. Zinchenko. Russ. J. Math. Phys. 12,443–471 (2005).

[185] “On the spectrum of Jacobi operators with quasi-periodic algebro-geometriccoefficients”; with V. Batchenko. Int. Math. Res. Papers No. 10, 511–563(2005).

[186] Fritz Gesztesy, Karl Unterkofler, and Rudi Weikard, An explicit character-ization of Calogero-Moser systems, Trans. Amer. Math. Soc. 358 (2006),no. 2, 603–656 (electronic), DOI 10.1090/S0002-9947-05-03886-9. MR2177033(2006h:35229)

[187] Fritz Gesztesy and Maxim Zinchenko, Weyl-Titchmarsh theory for CMVoperators associated with orthogonal polynomials on the unit circle, J. Ap-prox. Theory 139 (2006), no. 1-2, 172–213, DOI 10.1016/j.jat.2005.08.002.MR2220038 (2007f:47027)

[188] Fritz Gesztesy and Maxim Zinchenko, On spectral theory for Schrodinger op-erators with strongly singular potentials, Math. Nachr. 279 (2006), no. 9-10,1041–1082, DOI 10.1002/mana.200510410. MR2242965 (2007h:47076)

[189] Steve Clark and Fritz Gesztesy, On self-adjoint and J-self-adjoint Dirac-typeoperators: a case study, Recent advances in differential equations and mathe-matical physics, Contemp. Math., vol. 412, Amer. Math. Soc., Providence, RI,2006, pp. 103–140, DOI 10.1090/conm/412/07770. MR2259103 (2009d:47045)

[190] Fritz Gesztesy and Vadim Tkachenko,When is a non-self-adjoint Hill operatora spectral operator of scalar type?, C. R. Math. Acad. Sci. Paris 343 (2006),no. 4, 239–242, DOI 10.1016/j.crma.2006.06.014 (English, with English andFrench summaries). MR2245385 (2007b:34211)

[191]

2006:

“Local conservation laws and the Hamiltonian formalism for the Toda hierar-chy revisited”; with H. Holden. Trans. Roy. Norwegian Soc. Sci. Lett. (2006)(3), 1–30.

[192] Fritz Gesztesy and Peter Yuditskii, Spectral properties of a class of reflection-less Schrodinger operators, J. Funct. Anal. 241 (2006), no. 2, 486–527, DOI10.1016/j.jfa.2006.08.006. MR2271928 (2008a:34209)

[193] Fritz Gesztesy and Maxim Zinchenko, A Borg-type theorem associated withorthogonal polynomials on the unit circle, J. London Math. Soc. (2) 74 (2006),no. 3, 757–777, DOI 10.1112/S0024610706023167. MR2286444 (2007m:47071)

[194] Fritz Gesztesy, Yuri Latushkin, and Konstantin A. Makarov, Evans func-tions, Jost functions, and Fredholm determinants, Arch. Ration. Mech. Anal.186 (2007), no. 3, 361–421, DOI 10.1007/s00205-007-0071-7. MR2350362(2008k:34209)

[195] F. Gesztesy, M. Mitrea, and M. Zinchenko, Multi-dimensional versions of adeterminant formula due to Jost and Pais, Rep. Math. Phys. 59 (2007), no. 3,365–377, DOI 10.1016/S0034-4877(07)80072-3. MR2347795 (2009f:47020)

PUBLICATIONS OF FRITZ xxv

[196] Spectral theory and mathematical physics: a Festschrift in honor of Barry Si-mon’s 60th birthday, Proceedings of Symposia in Pure Mathematics, vol. 76,American Mathematical Society, Providence, RI, 2007. Ergodic Schrodingeroperators, singular spectrum, orthogonal polynomials, and inverse spectraltheory; Papers from the conference held at the California Institute of Technol-ogy, Pasadena, CA, March 27–31, 2006; Edited by Fritz Gesztesy, Percy Deift,Cherie Galvez, Peter Perry and Wilhelm Schlag. MR2307744 (2007m:00018)

[197] “Algebro-geometric finite-band solutions of the Ablowitz–Ladik hierarchy”;with H. Holden, J. Michor, and G. Teschl. Int. Math. Res. Notices 2007,rnm082, 1–55.

[198] Fritz Gesztesy, Marius Mitrea, and Maxim Zinchenko, Variations on atheme of Jost and Pais, J. Funct. Anal. 253 (2007), no. 2, 399–448, DOI10.1016/j.jfa.2007.05.009. MR2370084 (2008k:35081)

[199] Stephen Clark, Fritz Gesztesy, and Maxim Zinchenko, Weyl-Titchmarsh the-ory and Borg-Marchenko-type uniqueness results for CMV operators withmatrix-valued Verblunsky coefficients, Oper. Matrices 1 (2007), no. 4, 535–592, DOI 10.7153/oam-01-31. MR2363977 (2008h:34085)

[200] Fritz Gesztesy, Helge Holden, Johanna Michor, and Gerald Teschl, TheAblowitz-Ladik hierarchy revisited, Methods of spectral analysis in mathemati-cal physics, Oper. Theory Adv. Appl., vol. 186, Birkhauser Verlag, Basel, 2009,pp. 139–190, DOI 10.1007/978-3-7643-8755-6 8. MR2732077 (2012b:37174)

[201] Fritz Gesztesy, Marius Mitrea, and Maxim Zinchenko, On Dirichlet-to-Neumann maps and some applications to modified Fredholm determi-nants, Methods of spectral analysis in mathematical physics, Oper. The-ory Adv. Appl., vol. 186, Birkhauser Verlag, Basel, 2009, pp. 191–215, DOI10.1007/978-3-7643-8755-6 9. MR2732078 (2012b:47053)

[202] Fritz Gesztesy, Helge Holden, and Gerald Teschl, The algebro-geometric Todahierarchy initial value problem for complex-valued initial data, Rev. Mat.Iberoam. 24 (2008), no. 1, 117–182, DOI 10.4171/RMI/532. MR2435969(2010a:37133)

[203] Fritz Gesztesy and Helge Holden, Real-valued algebro-geometric solutions ofthe Camassa-Holm hierarchy, Philos. Trans. R. Soc. Lond. Ser. A Math.Phys. Eng. Sci. 366 (2008), no. 1867, 1025–1054, DOI 10.1098/rsta.2007.2060.MR2377684 (2009b:37128)

[204] Stephen Clark, Fritz Gesztesy, and Maxim Zinchenko, Borg-Marchenko-typeuniqueness results for CMV operators, Skr. K. Nor. Vidensk. Selsk. 1 (2008),1–18. MR2517327 (2010g:34008)

[205] Fritz Gesztesy, Helge Holden, Johanna Michor, and Gerald Teschl, Local con-servation laws and the Hamiltonian formalism for the Ablowitz-Ladik hier-archy, Stud. Appl. Math. 120 (2008), no. 4, 361–423, DOI 10.1111/j.1467-9590.2008.00405.x. MR2416645 (2009i:37156)

[206] Fritz Gesztesy, Konstantin A. Makarov, and Maxim Zinchenko, Essentialclosures and AC spectra for reflectionless CMV, Jacobi, and Schrodingeroperators revisited, Acta Appl. Math. 103 (2008), no. 3, 315–339, DOI10.1007/s10440-008-9238-y. MR2430447 (2010b:47118)

[207] Fritz Gesztesy, Yuri Latushkin, and Kevin Zumbrun, Derivatives of (modified)Fredholm determinants and stability of standing and traveling waves, J. Math.

xxvi PUBLICATIONS OF FRITZ

Pures Appl. (9) 90 (2008), no. 2, 160–200, DOI 10.1016/j.matpur.2008.04.001(English, with English and French summaries). MR2437809 (2012b:47035)

[208] Fritz Gesztesy and Marius Mitrea, Generalized Robin boundary conditions,Robin-to-Dirichlet maps, and Krein-type resolvent formulas for Schrodingeroperators on bounded Lipschitz domains, Perspectives in partial differentialequations, harmonic analysis and applications, Proc. Sympos. Pure Math.,vol. 79, Amer. Math. Soc., Providence, RI, 2008, pp. 105–173. MR2500491(2010k:35087)

[209] F. Gesztesy, A. Pushnitski, and B. Simon, On the Koplienko spectral shiftfunction. I. Basics, Zh. Mat. Fiz. Anal. Geom. 4 (2008), no. 1, 63–107, 202(English, with English and Ukrainian summaries). MR2404174 (2009k:47042)

[210] Fritz Gesztesy and Vadim Tkachenko, A criterion for Hill operators to bespectral operators of scalar type, J. Anal. Math. 107 (2009), 287–353, DOI10.1007/s11854-009-0012-5. MR2496408 (2010d:47063)

[211] Fritz Gesztesy and Marius Mitrea, Robin-to-Robin maps and Krein-type resol-vent formulas for Schrodinger operators on bounded Lipschitz domains, Mod-ern analysis and applications. The Mark Krein Centenary Conference. Vol.2: Differential operators and mechanics, Oper. Theory Adv. Appl., vol. 191,Birkhauser Verlag, Basel, 2009, pp. 81–113, DOI 10.1007/978-3-7643-9921-4 6. MR2569392 (2011a:35088)

[212] Fritz Gesztesy and Maxim Zinchenko, Local spectral properties of reflec-tionless Jacobi, CMV, and Schrodinger operators, J. Differential Equations246 (2009), no. 1, 78–107, DOI 10.1016/j.jde.2008.05.006. MR2467016(2009k:47085)

[213] Fritz Gesztesy, Mark Malamud, Marius Mitrea, and Serguei Naboko, Gen-eralized polar decompositions for closed operators in Hilbert spaces and someapplications, Integral Equations Operator Theory 64 (2009), no. 1, 83–113,DOI 10.1007/s00020-009-1678-x. MR2501173 (2010k:47007)

[214] Fritz Gesztesy and Marius Mitrea, Nonlocal Robin Laplacians and someremarks on a paper by Filonov on eigenvalue inequalities, J. DifferentialEquations 247 (2009), no. 10, 2871–2896, DOI 10.1016/j.jde.2009.07.007.MR2568160 (2010k:35079)

[215] Stephen Clark, Fritz Gesztesy, and Maxim Zinchenko, Minimal rank decou-pling of full-lattice CMV operators with scalar- and matrix-valued Verblun-sky coefficients, Difference equations and applications, Ugur-Bahcesehir Univ.Publ. Co., Istanbul, 2009, pp. 19–59. MR2664173 (2011i:47040)

[216] Fritz Gesztesy, Helge Holden, Johanna Michor, and Gerald Teschl,The algebro-geometric initial value problem for the Ablowitz-Ladik hi-erarchy, Discrete Contin. Dyn. Syst. 26 (2010), no. 1, 151–196, DOI10.3934/dcds.2010.26.151. MR2552783 (2010m:37126)

[217] Sergei Avdonin, Fritz Gesztesy, and Konstantin A. Makarov, Spectral esti-mation and inverse initial boundary value problems, Inverse Probl. Imaging 4(2010), no. 1, 1–9, DOI 10.3934/ipi.2010.4.1. MR2592779 (2011b:93038)

[218] “On Dirichlet-to-Neumann maps, nonlocal Interactions, and some applica-tions to Fredholm determinants”; with M. Mitrea and M. Zinchenko. FewBody Systems 47, 49–64 (2010).

[219] Mark S. Ashbaugh, Fritz Gesztesy, Marius Mitrea, Roman Shterenberg, andGerald Teschl, The Krein-von Neumann extension and its connection to an

PUBLICATIONS OF FRITZ xxvii

abstract buckling problem, Math. Nachr. 283 (2010), no. 2, 165–179, DOI10.1002/mana.200910067. MR2604115 (2011f:47078)

[220] Mark S. Ashbaugh, Fritz Gesztesy, Marius Mitrea, and Gerald Teschl, Spectraltheory for perturbed Krein Laplacians in nonsmooth domains, Adv. Math.223 (2010), no. 4, 1372–1467, DOI 10.1016/j.aim.2009.10.006. MR2581375(2011d:47052)

[221] S. Clark, F. Gesztesy, and M. Mitrea, Boundary data maps for Schrodingeroperators on a compact interval, Math. Model. Nat. Phenom. 5 (2010), no. 4,73–121, DOI 10.1051/mmnp/20105404. MR2662451 (2011e:34187)

[222] Fritz Gesztesy and Marius Mitrea, A description of all self-adjoint exten-sions of the Laplacian and Kreın-type resolvent formulas on non-smooth do-mains, J. Anal. Math. 113 (2011), 53–172, DOI 10.1007/s11854-011-0002-2.MR2788354 (2012d:47126)

[223] F. Gesztesy, I. Mitrea, D. Mitrea, and M. Mitrea,On the nature of the Laplace-Beltrami operator on Lipschitz manifolds, J. Math. Sci. (N. Y.) 172 (2011),no. 3, 279–346, DOI 10.1007/s10958-010-0199-0. Problems in mathematicalanalysis. No. 52. MR2839866

[224] Fritz Gesztesy and Helge Holden, The damped string problem revis-ited, J. Differential Equations 251 (2011), no. 4-5, 1086–1127, DOI10.1016/j.jde.2011.04.025. MR2812583 (2012e:35137)

[225] Fritz Gesztesy, Yuri Latushkin, Konstantin A. Makarov, Fedor Sukochev,and Yuri Tomilov, The index formula and the spectral shift function for rela-tively trace class perturbations, Adv. Math. 227 (2011), no. 1, 319–420, DOI10.1016/j.aim.2011.01.022. MR2782197 (2012c:47039)

[226] Fritz Gesztesy and Maxim Zinchenko, Symmetrized perturbation determi-nants and applications to boundary data maps and Krein-type resolventformulas, Proc. Lond. Math. Soc. (3) 104 (2012), no. 3, 577–612, DOI10.1112/plms/pdr024. MR2900237

[227] Fritz Gesztesy, Alexander Gomilko, Fedor Sukochev, and Yuri Tomilov, Ona question of A. E. Nussbaum on measurability of families of closed lin-ear operators in a Hilbert space, Israel J. Math. 188 (2012), 195–219, DOI10.1007/s11856-011-0120-7. MR2897729

[228] Fritz Gesztesy, Jerome A. Goldstein, Helge Holden, and Gerald Teschl,Abstract wave equations and associated Dirac-type operators, Ann. Mat.Pura Appl. (4) 191 (2012), no. 4, 631–676, DOI 10.1007/s10231-011-0200-7. MR2993967

[229] “Weak convergence of spectral shift functions for one-dimensional Schrodingeroperators”; with R. Nichols. Math. Nachrichten 285, 1799–1838 (2012).

[230] Fritz Gesztesy and Roger Nichols, An abstract approach to weak convergenceof spectral shift functions and applications to multi-dimensional Schrodingeroperators, J. Spectr. Theory 2 (2012), no. 3, 225–266. MR2947287

[231] Fritz Gesztesy and Vadim Tkachenko, A Schauder and Riesz basis crite-rion for non-self-adjoint Schrodinger operators with periodic and antiperiodicboundary conditions, J. Differential Equations 253 (2012), no. 2, 400–437,DOI 10.1016/j.jde.2012.04.002. MR2921200

[232] “Initial value problems and Weyl–Titchmarsh theory for Schrodinger oper-ators with operator-valued potentials”; with R. Weikard and M. Zinchenko.Operators and Matrices 7, 241–283 (2013).

xxviii PUBLICATIONS OF FRITZ

[233] “On a class of model Hilbert spaces”; with R. Weikard and M. Zinchenko.Discrete and Continuous Dynamical Systems (to appear).

[234] “Heat kernel bounds for elliptic partial differential operators in divergenceform with Robin-type boundary conditions”; with M. Mitrea and R. Nichols.J. Analyse Math. (to appear).

[235] “Boundary data maps and Krein’s resolvent formula for Sturm–Liouville op-erators on a finite interval”; with S. Clark, R. Nichols, and M. Zinchenko.Preprint 2012.

[236] “Supersymmetry and Schrodinger-type operators with distributional matrix-valued potentials”; with J. Eckhardt, R. Nichols, and G. Teschl. Preprint2012.

[237] “Weyl–Titchmarsh theory for Sturm–Liouville operators with distributionalcoefficients”; with J. Eckhardt, R. Nichols, and G. Teschl. Opuscula Math.(to appear).

[238] “A survey on the Krein–von Neumann extension, the corresponding ab-stract buckling Problem, and Weyl-type spectral asymptotics for perturbedKrein Laplacians in nonsmooth domains”; with M. Ashbaugh, M. Mitrea, R.Shterenberg, and G. Teschl. Advances in Partial Differential Equations, M.Demuth and W. Kirsch (eds.), Birkhauser, Basel, (to appear).

[239] “Inverse spectral theory for Sturm–Liouville operators with distributional co-efficients”; with J. Eckhardt, R. Nichols, and G. Teschl. Preprint 2012.

[240] “On stability of square root domains for non-self-adjoint operators under ad-ditive perturbations”; with S. Hofmann and R. Nichols. Preprint 2012.

[241] “On spectral theory for Schrodinger operators with operator-valued poten-tials”; with R. Weikard and M. Zinchenko. Preprint 2013.

[242] “Stability of square root domains for one-dimensional non-self-adjoint second-order linear differential operators”; with S. Hofmann and R. Nichols. Preprint2013.

[243] “Some remarks on the spectral problem underlying the Camassa–Holm hier-archy”; with R. Weikard. Preprint 2013.

[244] “The Birman–Schwinger principle and eigenvalue multiplicity questions revis-ited”; with H. Holden. Preprint 2013.

MONOGRAPHS

Solvable Models in Quantum Mechanics; with S. Albeverio, R. Høegh-Krohn,and H. Holden. Texts and Monographs in Physics, Springer-Verlag, Heidelberg–New York, 1988, 452 pages. (Translated into Russian by Yu. A. Kuperin, K.A. Makarov, and V. A. Geiler, Mir Publishers, Moscow, 1991.) MR0926273(90a:81021)

The second and expanded edition of this monograph appeared as:Solvable Models in Quantum Mechanics, 2nd edition; with S. Albeverio, R.Høegh-Krohn, and H. Holden. AMS–Chelsea Series, Amer. Math. Soc., 2005,488 pages. With an appendix by P. Exner. MR2105735

PUBLICATIONS OF FRITZ xxix

Soliton Equations and Their Algebro-Geometric Solutions. Vol. I: (1 + 1)-Dimensional Continuous Models; with H. Holden. Cambridge Studies in Ad-vanced Mathematics, Vol. 79, Cambridge Univ. Press, Cambridge, 2003, 505pages. MR1992536

Soliton Equations and Their Algebro-Geometric Solutions. Vol. II: (1 + 1)-Dimensional Discrete Models; with H. Holden, J. Michor, and G. Teschl.Cambridge Studies in Advanced Mathematics, Vol. 114, Cambridge Univ.Press, Cambridge, 2008, 438 pages. MR2446594

VOLUMES CO-EDITED

Continued Fractions: From Analytic Number Theory to Constructive Approx-imation, B. C. Berndt and F. Gesztesy (eds.), Contemporary Mathematics236, Amer. Math. Soc., Providence, RI, 1999, 379 pages. MR1665358(2000d:00018)

Stochastic Processes, Physics and Geometry: New Interplays. I. A Volume inHonor of Sergio Albeverio, F. Gesztesy, H. Holden, J. Jost, S. Paycha, M.Rockner, and S. Scarlatti (eds.), Canadian Mathematical Society ConferenceProceedings, Vol. 28, Amer. Math. Soc., Providence, RI, 2000, 333 pages.MR1803374

Stochastic Processes, Physics and Geometry: New Interplays. II. A Volumein Honor of Sergio Albeverio, F. Gesztesy, H. Holden, J. Jost, S. Paycha, M.Rockner, and S. Scarlatti (eds.), Canadian Mathematical Society ConferenceProceedings, Vol. 29, Amer. Math. Soc., Providence, RI, 2000, 647 pages.MR1803398

Spectral Theory and Mathematical Physics: A Festschrift in Honor of BarrySimon’s 60th Birthday: Quantum Field Theory, Statistical Mechanics, andNonrelativistic Quantum Systems, F. Gesztesy, Managing Editor, P. Deift,C. Galvez, P. Perry, and W. Schlag (eds.), Proceedings of Symposia in PureMathematics, Vol. 76.1, Amer. Math. Soc., Providence, RI, 2007, 496 pages.MR2310192

Spectral Theory and Mathematical Physics: A Festschrift in Honor of BarrySimon’s 60th Birthday: Ergodic Schrodinger Operators, Singular Spectrum,Orthogonal Polynomials, and Inverse Spectral Theory, F. Gesztesy, ManagingEditor, P. Deift, C. Galvez, P. Perry, and W. Schlag (eds.), Proceedings ofSymposia in Pure Mathematics, Vol. 76.2, Amer. Math. Soc., Providence, RI,2007, 464 pages. MR2307744

xxx PUBLICATIONS OF FRITZ

JOURNAL ISSUES CO-EDITED

Mathematische Nachrichten, 283, Nos. 1–3 (2010), Erhard Schmidt MemorialIssue, Parts I–III, A. Bottcher, F. Gesztesy, and R. Mennicken (eds.), Wiley-VCH, pp. 1–159, 161–329, and 331–499.

The Mathematical Modelling of Natural Phenomena (MMNP), 5, No. 4 (2010),Spectral problems. Issue dedicated to the memory of M. Birman, N. Apreute-sei, D. Damanik, Yu. Egorov, F. Gesztesy, P. Kurasov, A. Laptev, S. Naboko,V. Volpert, V. Voulgalter (eds.), Cambridge University Press and EDP Sci-ences, pp. 1–469.

Mathematische Nachrichten, 285, No. 14–15 (2012), Eduard R. TsekanovskiiSpecial Issue on the Occasion of his Seventy-Fifth Birthday, F. Gesztesy, H.Langer, M. Malamud, and R. Mennicken (eds.), Wiley-VCH, pp. 1671–1931.

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